Recently, entropy-stable DG schemes
have emerged as a way to construct
high-order discretizations with rigorous nonlinear stability estimates
in a parameter-free fashion [1]}, [2]}.
Namely, semi-discrete entropy stability estimates are guaranteed by using
specially constructed numerical fluxes [3]} and
flux-differencing [4]}.
Importantly, the schemes are computationally affordable because they do not rely
on exact integration but instead exploit the
summation-by-parts property of polynomial differentiation operators [5]}.
Following the pioneering work in [6]}, [7]}
for the compressible Euler equations, the class of entropy-stable DG
schemes has been extended
to general systems of nonlinear conservation laws by [8]}.
[9]}, [10]} generalized this to
“modal” DG formulations which do not satisfy
summation-by-parts.
Most entropy stable DG schemes are constructed assuming exact integration in
time, and [11]} achieved fully discrete entropy-stability using
relaxation Runge–Kutta time integrators.
